IMPROVING MATHEMATICS SKILLS USING DIFFERENTIATED INSTRUCTION WITH PRIMARY AND HIGH SCHOOL STUDENTS Daniel K. Ellis, B.A. Kerry A. Ellis, B.S. Linda J. Huemann, B.A. Elizabeth A. Stolarik, B.A. An Action Research Project Submitted to the Graduate Faculty of the School of Education in Partial Fulfillment of the Requirement for the Degree of Master of Arts in Teaching and Leadership Saint Xavier University & Pearson Achievement Solutions, Inc. Field-Based Master’s Program Chicago, Illinois June, 2007
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IMPROVING MATHEMATICS SKILLS USING DIFFERENTIATED INSTRUCTION
WITH PRIMARY AND HIGH SCHOOL STUDENTS
Daniel K. Ellis, B.A. Kerry A. Ellis, B.S.
Linda J. Huemann, B.A. Elizabeth A. Stolarik, B.A.
An Action Research Project Submitted to the Graduate Faculty of the
School of Education in Partial Fulfillment of the
Requirement for the Degree of Master of Arts in Teaching and Leadership
Saint Xavier University & Pearson Achievement Solutions, Inc.
Field-Based Master’s Program
Chicago, Illinois
June, 2007
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TABLE OF CONTENTS
ABSTRACT ………………………………………………………………………… iii CHAPTER 1: PROBLEM STATEMENT AND CONTEXT ……………………… 1 General Statement of the Problem …………………………………………… 1 Immediate Context of the Problem …………………………………………… 1 Local Context of the Problem ………………………………………………… 10 National Context of the Problem ……………………………………………… 14 CHAPTER 2: PROBLEM DOCUMENTATION ……………………………………. 15 Evidence of the Problem ………………………………………………………. 15 Probable Causes ……………………………………………………………….. 35 CHAPTER 3: THE SOLUTION STRATEGY ……………………………………….. 44 Review of the Literature ……………………………………………………….. 44 Project Objective and Processing Statements ………………………………….. 57 Project Action Plan ……………………………………………………………... 58 Methods of Assessment ………………………………………………………… 59 CHAPTER 4: PROJECT RESULTS …………………………………………………… 61 Historical Description of the Intervention ………………………………………. 61 Presentation and Analysis of Results ……………………………………………. 76 Conclusions and Recommendations ……………………………………………… 79 REFERENCES …………………………………………………………………………… 82 APPENDICES …………………………………………………………………………… 86 Appendix A: Teacher Survey….……………………………………………….. 87 Appendix B: High School Student Survey…………………………………….. 88
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Appendix C: Kindergarten Student Survey………………………………….. 89 Appendix D: Second Grade Student Survey………………………………… 90 Appendix E: High School Pre- and Post-Tests……………………………… 91 Appendix F: Kindergarten Pre- and Post-Tests…………………………….. 95 Appendix G: Second Grade Pre- and Post-Tests……………………………. 97 Appendix H: Student Observation Checklist………………………………... 100 Appendix I: Sample High School Multi-tiered Worksheet...……………….. 101
Appendix J: Kindergarten Work Sample from a Differentiated Lesson…….. 107
Appendix K: Sample Second Grade Multi-tiered Worksheet...……………… 108
Appendix L: Sample Second Grade Multi-tiered Worksheets...……………… 109
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ABSTRACT
Varied academic ability is a problem across the country and is the focus of this action research project report. The four teacher researchers were searching for way to reach all learners with their mathematics instruction. The purpose of the research was to increase mathematical performance in a varied ability math classroom. To address varied ability levels in the classroom, the teacher researchers implemented differentiation instruction and modified three areas of instruction: curriculum, strategies, and student work. The research project was implemented on January 29, 2007 and concluded on May 11, 2007. The participants consisted of 79 math students: 26 grade 10-12 high school students, 53 kindergarten through second grade students, and 25 teachers, for a total of 104 participants. Today’s students enter the classroom with different learning experiences and prior knowledge. The teacher researchers encountered academic achievement that ranged from high, medium, and low. The students that performed at a high academic level were often finished with their work early and often left unchallenged. The students that performed below average academically needed constant support and redirection which took away from the teacher’s instruction time. The only students that were benefiting were the average students. This research project used a student survey, teacher survey, observation checklist, and pre-test and post-tests to document the problem and found the above to be true. The interventions consisted of cooperative learning lessons, multiple intelligence based lessons, student choice of assignments, and differentiated assignments. Cooperative learning is one way in which teachers can help students learn to work with one another. It allows students to work in groups to achieve a goal. Implementing lessons using Howard Gardner’s Multiple Intelligences was another intervention used. Gardner suggests that each individual has the ability to learn in many different ways, yet we all have one preferred learning style. Student choice encourages students to be in charge of their own learning and help them to gain a better sense of personal and social responsibility (Betts, 2004; George, 2005). One way to accommodate for the many levels in today’s classrooms is to differentiate assignments to suit individual needs. After reviewing the results of the pre- and post-test data the four teacher researchers noticed a marked change in student performance. However, it was not possible to determine if student success was based on interventions or the fact that the teachers had covered the concepts with the class between testing. Since the pre-tests focused on concepts that had not been covered it is believed that presenting the material would inevitably lead to student progress. The positive change in student performance led us to believe that our interventions were effective in some way. It is believed cooperative learning positively impacted student progress and the teacher researchers plan to continue implementing this strategy. In conclusion, each teacher researcher would like to continue to implement differentiation. With the varied abilities in today’s classroom it is necessary to adapt teaching methods to meet different needs. Differentiation is something that cannot be implemented immediately and needs to be well thought out, planned, and gradually implemented. Each teacher researcher felt the frustrations of planning time, time allotted for activities in the classroom, and changing teaching styles in the middle of the year. It is believed these frustrations can be alleviated through proper training and resources.
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CHAPTER 1
PROBLEM STATEMENT AND CONTEXT
General Statement of the Problem
Reaching every student in an inclusion classroom was the problem identified by the four
teacher researchers. Several behaviors were observed that could define multiple abilities in the
classroom as a problem. The teacher researchers encountered academic achievement that ranged
from high, medium, and low. The students that performed at a high academic level were often
finished with their work early and often left unchallenged. The students that performed below
average academically needed constant support and redirection which took away from the
teacher’s instruction time. The only students that were benefiting were the average students.
To identify that multiple abilities in the classroom exist, the teacher researchers
developed four tools. The first tool that was created was a checklist to document on task and off
task behavior. The second tool that was created was a student survey. The survey was developed
to identify that students have different interest and that students might learn better if their interest
were addressed in the learning process. The third tool that was created was a teacher survey. This
was utilized to determine that multiple abilities is a common problem among teachers. The final
tools that were developed were a pre- and post-test. These tools were created to assess the
students’ academic performances before and after interventions were implemented.
Immediate Context of the Problem
This action research was conducted by four teacher researchers at two different sites. Site
A was a suburban primary school with one teacher researcher at the kindergarten level and two
teacher researchers at the second grade level. One teacher researcher was at Site B teaching high
school level mathematics.
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Site A
Site A is a suburban primary school, and the teacher researchers teach kindergarten and
second grades. Unless otherwise noted, the information in this section was retrieved from the
Illinois School Report Card, 2005 and the 2005 Illinois School Profile.
Table 1 below identifies the ethnic backgrounds of the student body at Site A. As seen in
this table, the majority of the student body at Site A consisted of Caucasian students.
Table 1
Racial/Ethnic Background by Percentage
Caucasian
Hispanic
Asian
African American
Native American
School 72.2 14.6 5.7 5.5 2.0 District 80.3 12.3 4.2 2.6 0.5
Site A has a total enrollment of 508 students, with the district enrollment of 1,130. This
enrollment included students from kindergarten through third grade. The low-income rates at
Site A were 5.3% compared to 6.1% for the district. At Site A the students identified with
Limited English Proficiency were 7.5 % and the district level was 4.6%. The mobility rate at Site
A was 26.7% compared to 18.9% for the district. Site A had an attendance rate of 94.5% and
while the district had 94.8%.
The number of full-time teachers at Site A was not reported on the 2005 school report
card. However, according to the data from the staff information posted on the Site A website,
(n.d., Site A staff contact information) teacher researchers calculated there were 21.5 full-time
teachers during the 2005-2006 school year. Females make up 100% of the staff. The average
teaching experience is 8.4 years for the district, with an average salary of $44,430. Teachers with
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bachelor’s degrees make up 55.8% (n = 12) of the district while those with a master’s degree or
above make up 44.2% (n = 10) (Site A Illinois School Report Card, 2005). The district student-
teacher ratio is 17.7:1 and the student-administrator ratio is 255.3:1. Due to lack of information
presented in the district report card, teacher researchers have calculated the average class size in
kindergarten was 21, first grade was 27, second grade was 27, and third grade was 25 during the
2005-2006 school year.
Site A has one superintendent who overseas three schools. Serving under the
superintendent were two principals. Site A was administered by one of the principals.
Administrative support consists of two secretaries, one food service coordinator, and one
custodian. Academic support includes one special education coordinator, one special education
teacher, three Regular Education Initiative (REI) teachers, one reading specialist, one English
Language Learner (ELL) teacher, two speech therapists, and one special service teacher. Special
Education District of Lake County (SEDOL) employees includes one occupational therapist, one
hearing itinerant, two social workers, and two psychologists. General education teachers include
3.5 kindergarten teachers, seven first grade teachers, six second grade teachers, and five third
grade teachers. As the population grows, it is projected that for the 2006-2007 school year,
kindergarten, second, and third grades will be adding one classroom per grade level. Site A
employs one special teacher for the following subject areas: computers, physical education, art,
music, and two librarians.
The core subjects taught in kindergarten through grade 3 consist of mathematics, science,
English/language, and social science. According to the Illinois State School Report Card for
grade 3, time devoted to teaching core subjects in the targeted school included 60 minutes of
mathematics, 30 minutes of science, 170 of English/language arts, and 30 minutes of social
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science in a day. Kindergarten is the exception with 300 contact minutes devoted for students per
week (Building Principal, personal communication, June 27, 2006).
The students in the district take the Illinois Standards Achievement Test yearly. Reading,
writing, and mathematics are tested in grades three and five while science is tested in grade four.
The overall performance of third graders for the 2004-2005 school year reported that the targeted
district had 68.3% of the students meeting or exceeding the Illinois Learning Standards in
reading. This 68.3% is compared to 66.6% for the state. In mathematics, 79.7% of students in the
district met or exceeded the Illinois Learning Standards. This 79.7% is compared to 79.2% for
the state. In addition, students enrolled in a comprehensive ELL program take the Illinois
Measure of Annual Growth in English (IMAGE) exam. The overall performance for the 2004-
2005 school year reported that the targeted district had 75.0% of the students meeting or
exceeding the Illinois Learning Standards. This 75.0% is compared to 49.3% for the state.
The targeted school also takes part in an annual grade level standardized test developed
by the Scholastic Testing Service, Inc. Table 2 below shows the breakdown on performance
scores by grade level. The benchmark score for each grade level is: the grade level plus .8 (which
indicates the month, April, of the school year when the test was administered). Thus, the
benchmark score for first grade would be 1.8; for second grade 2.8; and for third grade 3.8.
Table 2
Benchmark Scores: Grades 1-3
Language Math Science Social Science Grade 1 2.2 2.4 1.9 2.1 Grade 2 3.1 3.1 3.0 3.1 Grade 3 3.9 4.2 3.9 4.1
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Site A is located at the intersection of two rural streets on a large area of grassland
purchased by the district many years ago. Construction has been in progress during the last two
years and will culminate at the end of 2006 resulting in a beautiful, large campus that
encompasses all three of the schools located in our district (one primary building, one elementary
building, one middle school building). Our building is a single story brick structure (with the
exception of the two-story middle school) that houses over 1,130 students (K-8). The targeted
site welcomes students and families into a large spacious office which includes a principal’s
office, work room, and nurse’s station. The building is broken up by grade level pods where all
grade level classrooms are clustered together and share a large common area where classes are
invited to work with one another. We have a well-stocked library, two computer labs, and
cafeteria with kitchen, conference room, teacher’s lounge, music room, and art room enclosed by
a floor to ceiling glass wall.
Site A is unique due to a large nature center that is on school grounds. This nature center
is an educational tool in that it is used to teach students about plant growth and animal habitats.
Each classroom is assigned a garden area to observe and maintain throughout the school year.
We believe that there are many factors contributing to the varied abilities in the
classroom. Site A is located in an area that has two different socioeconomic backgrounds. We
feel that one particular area of the district may be less affluent which in turn leads to parents
working more. The more affluent areas tend to have one parent at home who is able to partake in
their child’s education both at home and school. Along with socioeconomic status, each student’s
educational background is different. The district does not offer regular education preschool
classes to prepare the students for kindergarten. When students enter kindergarten varied ability
is already prevalent and the gaps are difficult to close throughout their years of education. The
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state of Illinois has not mandated kindergarten. Thus, students can enter first grade with no prior
school experience.
Site B
All of the following information is provided in the 2005 Illinois School Report Card, Site
B, unless otherwise noted. The fourth teacher researcher teaches high school mathematics at Site
B which is an upper middle class suburb of Chicago. The total enrollment at Site B is 2,124
students. The ethnic break down is noted in Table 3 below and demonstrates the school is
overwhelming Caucasian with a much smaller percentage of Hispanic students compared to Site
A.
Table 3
Racial/Ethnic Background by Percentage of Site B
Caucasian HispanicAsian/Pacific
IslanderAfrican
AmericanMultiracial/
EthnicNative
American
92.3 4.1 2.3 .7 .5 .1
Of the 2,124 students at site B, less than 1% are categorized as ELL. Only 3% are considered as
coming from a low-income family or qualify for free and reduced lunches compared to 40% state
wide. Approximately .1% of the students at Site B are considered chronically truant. The
mobility rate in this high school is only 5.4% compared to 16.1% statewide. The attendance rate
at this site is very good with 96.1% of students attending school on a daily basis.
There are 417 teachers working within the entire district and a total of 141 teachers
working at Site B. Although no further information was given on just the high school, the
average salary of teachers in the entire school district is $58,881, with an average of 11.5 years
of experience. Also, 41.3% (n = 172) of the district’s teachers have bachelor’s degrees and
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58.7% (n = 245) have master’s degrees or above. There is a student teacher ratio of 18.7 and an
average class size of 19.8 at the high school. Lastly, there is a 98% parent contact rate at the high
school which includes parent teacher conferences, visits to the school or school visiting the
home, telephone conversations or written correspondence.
Regarding the academic program at Site B, the school prides itself on preparing students
for college and that mission guides the curriculum to a great extent. The graduation requirements
have recently changed. A committee was formed regarding increasing the requirements in 2005
and its recommendations were accepted and implemented just before the state of Illinois raised
the requirements for high school graduation across the board. The changes are being phased in
over the next four years but the current requirements for students, according to the high school’s
Student Handbook, is 22 credits. Of the 22 credits, students must earn three credits in English,
two in math, two in science, two and one-half credits in social studies, one credit of humanities,
and one-half credit in each consumer education and health. In addition to the above credits,
graduates must be enrolled in a physical education course every single semester, complete the
Prairie State Achievement Exam (PSAE), and also complete a driver’s education course. Overall,
the high school has a very high graduation rate of 97.8% compared to the state average of 87.4%.
The average PSAE score is modest 71.2 compared to a 54.9 average statewide.
Site B has 199 staff members total, 141 teachers including 11 applied arts, 20 English, 11
fine arts, 12 foreign language, 18 mathematic, 16 physical education, 20 science, 15 social
studies, and 18 special education. The administrative staff is broken down into one principal,
three assistant principals, two deans of discipline, one athletic director, one registrar, and nine
department chairs. The teacher support staff consists of one in-school suspension supervisor and
11 secretaries, including two for attendance, four for athletics, one for the dean’s office, three for
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the main office and administrators, and one for pupil personnel services. The student support
staff consists of seven guidance counselors, two nurses, two social workers, one college
counselor, three librarians, one SEDOL itinerant, one school psychologist, one speech
pathologist, one occupational therapist, and one police liaison. The building support staff
consists of four security, three technology support, and one head custodian in charge of
maintenance.
The members of Site B’s community recently passed a large referendum to remodel
outdated science laboratories, add a larger auditorium, and add additional classroom space to the
existing building which was under great pressure from increased student enrollment. The new
auditorium was designed for the renowned theater and performing arts program and is used
frequently throughout the year for some very impressive musicals and orchestra performances.
Depending on which one of the 20 entrances you walk through at the sprawling Site B,
you may gain a very different impression. If you enter through the southeast part of the building
the doors and airlocks are old and painted over many times. There are many murals painted on
the walls and student artwork is abundant in an attempt to spruce up the building. If entering
through the newer section that includes one finds the new field house is flush with trophies and
plaques and pictures of alumni that have excelled in all sports. Although it is a new structure,
anyone walking through the building would still feel a connection to past and the students that
make up a part of Site B’s history. If entering through the new auditorium’s entrance, a visitor
would be really be impressed with the exceptional artwork posted by the fine arts department in
the display cases in the hallway and you will find it hard to believe you are in a high school when
you walk in to the new auditorium itself. The architects claimed that this was by far the most
sophisticated auditorium in any high school in Illinois and outside of a few newer auditoriums on
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college campuses, it was probably the best in the state. The four-story auditorium’s stage
contains an elevator that descends into the orchestra pit, and a full-time lighting director has been
hired to run the facility! The school is completely wireless in all but a few areas so teachers may
take their laptops anywhere in the building and not lose any internet-based programs. There are
numerous dedicated computer laboratories that may be reserved by teachers as well as wireless
internet carts that may be taken into rooms for use. Walking in to the library a visitor will no
doubt find many students surfing the web or doing research. Walking down the newest science
wing visitors will find a fully equipped AutoCAD lab with computers, wind tunnel, and model
electrical circuits.
As demonstrated from the large referendum that was passed to upgrade the facilities, I
believe Site B has undergone some major changes in the makeup of the community in the last 20
years. A mostly blue-collar, working class community is becoming replaced by affluent, white-
collar families. Today, many families are putting an emphasis on education and increasing their
taxes to fund the education of their children. I believe this shift has led to a major increase in the
number of college level classes, advanced placement courses, and honors tracks to better prepare
students for college. While many students are on the fast track to college taking as many
advanced courses as they can, some students are planning to attend trade schools or community
college after high school and are taking remedial courses. I believe this growing disparity
between student coursework, in combination with divergent plans after high school, has directly
contributed to the varied ability that teachers see in the classroom.
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Local Context of the Problem
For the demographics of the region in which the teacher researchers are employed,
statistics used throughout this paper will be from the common county in which Site A and B are
located. The county is very diverse in economic terms and will mirror the diverse communities
that the two sites serve. Site B is varied in economic terms but is much more affluent in general
compared to Site A. Together, these sites provide a diverse spectrum which is very representative
of the entire county ranging from low-income to extremely high-income families. Site A is
located in the western region of the county and growing rapidly. The suburbs of Chicago are
pushing outwards every year and Site A is on the cusp of new development. Site B, which is
located in the southwest corner of the county, has already gone through rapid growth and
suburbanization because it is closer to Chicago.
According to the 2004 United States Census Bureau, the total population of the county in
which Sites A and B serve was 675,050 and is growing at a rate of 1.17% every year. The
median household income was $70,347 and 5.2% of the population’s families are below the
poverty level. As can be seen from the age distributions found in Table 4, a majority (70.6%, n =
454,992) of residents are between the ages of 18 and 65.
Table 4
Age Distributions of County by percentage
Persons under five years
Persons between 5 and 18
Persons between 18 and 65 Persons 65 and older
7.7 12.8 62.3 8.6
Ethnicity distributions are found in Table 5 showing an overwhelming percentage of Caucasian
residents with a sizeable Hispanic and Latino population.
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Table 5
Ethnic Distributions of County by percentage
Caucasian
Hispanic or Latino
African American Other
Asian
Two or
more races
American Indian and
Alaska Native
Native
Hawaiian and other Pacific Islander
80.9 17.6 6.2% 5.9 5.3 1.4 .2 .1
High school graduates, age 25 or older make up 88% of the population, while 42.1% of the
county’s population hold a bachelor’s degree or higher.
In the average household of this county, there are 2.99 people. The employment rate is
70.8%.Table 6 shows the diverse workforce of the county aged 16 years or older. This data
shows that the majority (41.7%) of people in this age group have a management, professional, or
related position.
Table 6
Types of Employment Within the County by percentage
Management,
professional, and related
occupations
Sales and office
occupationsService
occupations
Production, transportation, and material moving
occupations
Construction,
extraction, maintenance and
repair occupations
41.7 28.0 13.3 9.4 7.4
According to the Suburban Chicago Newspaper, the total crimes committed in 2004 within the
county were 2,909 per 100,000 residents.
The county is located on the shore of Lake Michigan spanning north of Chicago to the
Wisconsin border and west to the Chain-O-Lakes. The county is native to Potawatomie Indians
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and was recognized as a settlement by Illinois State Legislature in 1839 (Encyclopedia of
Chicago, 2005; Lake County Illinois Local Government, n.d., History of Lake County). The
county began as a trading and farming community but was transformed with the installation of
major roadways and railroads (Encyclopedia of Chicago, 2005). Today, the county is a mixture
of progressing urban areas and scenic rural communities. The county has numerous places of
interest. Recreational activities include numerous state parks, a super-regional shopping mall,
and the theme park Six Flags Great America. Two professional sports teams have their practice
facilities located in this county. Improvements in this county include preservation, expansion,
and modernization projects of bike paths, roadways, and railroads (Lake County Illinois Local
Government n.d., Quick facts about Lake County: Five year highway improvement plan). The
largest employers of this county include the Great Lakes Naval Training Center, Abbott
Laboratories, Hewitt Associates, Motorola, and Kemper Insurance Company (Encyclopedia of
Chicago, 2005).
At Site A, the district’s middle school, including three other middle schools in the area,
feed into one high school. The district’s mission statement at Site A is “…to foster excellence in
education so that its students will be able to reach their full potential and enhance their quality of
life in an ever-changing society” (Site A School District, n.d., paragraph 2). In the 2006-2007
school year, the district will have one primary building (kindergarten through second), one
elementary building (third through fifth), and one middle school building (sixth through eighth).
The district is overseen by one superintendent. The local property taxes are 70% of the schools
revenue. The 2002 total school tax rate per $100 dollars was 2.31. The 2003-2004 instructional
expenditure per pupil was $3,230. The operating expenditure per pupil was 6,419 (Illinois State
Board of Education, n.d., 2005 Illinois school report card). Between 2001-2003 the school
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district attempted to pass three building referendums. During the fall of 2004 the school districts’
building referendum passed (Illinois Association of School Administrators, n.d.). The district is
currently building two new buildings on existing land next to the primary building. Each
building is equipped with a computer laboratory. One computer is also provided for each
classroom with Internet access.
Site B is considered a unit school district. It has six elementary schools that feed into two
middle schools that in turn feed into one high school. The districts mission statement at Site B is
“to inspire all students to be passionate, continuous learners and to prepare them with the skills
to achieve their goals and flourish as responsible, caring citizens in a global community”
(Community School District 95, n.d.). There is one superintendent for the district. The local
property taxes are 80.5% of the schools revenue. The 2002 total school tax rate per $100 was
4.37. The 2003-2004 instructional expenditure per pupil was $5,134. The 2003-2004 operating
expenditure per pupil was 8,723 (Illinois State Board of Education, n.d., Illinois school report
card). There was a building referendum that was passed in fall 2000 (Illinois Association of
School Administrators, n.d.). This referendum provided the school with a field house,
auditorium, and equipment for the science department. Technology is a huge component of Site
B. The district provides computer laboratories, a lap top for each teacher, and each classroom
provides the students ample opportunities to use technologies.
We believe the various demographics of the county directly relate to the different values
placed upon education. As the residents of Chicago continue to spread further into the suburbs,
many households have parents working multiple jobs or two-income homes. With both parents
working, there is little time available for parents to interact on an educational level with their
children. This is one factor that we believe contributes to the varied abilities in our classrooms.
14
National Context of the Problem
Teachers are having difficulty accommodating disabilities, linguistic challenges, and
other unique abilities in their classrooms. Special education teachers, along with other support
staff, are concerned that the students they see on a daily basis are not receiving the proper
support in the classroom (Ferguson, 1999). Teachers do not know how to appropriately
implement lessons that will allow all students to reach their full potential (Holloway, 2000).
Varied ability is a problem across the country. Teachers are searching for way to reach all
learners in their classrooms. To address varied ability levels in the classroom, the teacher
researchers will implement differentiation instruction and modify three areas of instruction:
curriculum (content), strategies (process), and student work (product). Additionally, research
literature argues that teachers who want to reach all learners should also appeal to students’
multiple intelligences, and engage students through their interests (Tomlinson, 1999). Thus,
researchers will survey students to discover student interests and individual learning styles.
Finally, the success of differentiated instruction hinges on continually assessing students to
monitor their individual progress.
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CHAPTER 2
PROBLEM DOCUMENTATION
Evidence of the Problem
The purpose of the research was to increase mathematical performance in a varied ability
math classroom. Our pre-documentation data is looking to validate the fact that multiple abilities
exist in the classroom and the challenge this presents for inclusion teachers. The problem of
varied abilities appeared to be an issue among the four teacher researchers. The evidence was
documented by a teacher survey, student survey, observation checklist, and pre-test and post-
tests. These four tools were utilized from January 29, 2007 through May 11, 2007. The
participants consisted of 79 math students: 26 grade 10-12 high school math students, 53
kindergarten through second grade math students and 25 teachers for a total of 104 participants.
Teacher Survey
The purpose of this instrument was for the teacher researchers to determine the extent to
which teachers felt comfortable with differentiating instruction in mathematics. Teachers at Site
A and Site B were asked by the teacher researches to complete a teacher survey regarding the use
of differentiation strategies while teaching mathematics. Teachers were given two weeks to
complete the survey. Completed surveys were anonymously returned to a teacher researcher’s
mailbox at the appropriate sites. Surveys were collected at the end of each day and kept in a
central, confidential location. The researchers wanted to verify if teachers had the necessary
tools, time, and materials for effective differentiation. Keeping one particular class in mind,
teachers were asked to rate four questions using a Likert scale. The scale provided choices
ranging from (1) strongly agree to (4) strongly disagree. In addition, teachers were asked one
open ended question regarding the frustrations felt while teaching mathematics. Surveys were
16
distributed once on Monday, January 29, 2007 to15 primary teachers at Site A and 17 math
teachers at Site B. Surveys were distributed through teacher mailboxes. At Site A, 10 out of the
15 surveys were returned, a 67% response rate. At Site B, 15 out of 17 surveys were returned for
a response rate of 88%. Data was collapsed by combining strongly agree and agree into a single
category of agree while responses of strongly disagree and disagree were combined into a
disagree category. Teacher responses from Site A and B were combined using this method to
show a clearer correlation between agree and disagree. Please refer to Appendix A to view the
teacher survey.
The first question on the survey asked teachers if there was a wide range of math ability
in the classroom. The majority of teachers (92%, n = 23) agree that there is a wide range of
ability in their classroom.
Agree 92%
Disagree 8%
Figure 1: Wide Range of Ability in Classroom (n=25)
The second survey question asked if teachers felt like their instruction meets the needs of
learners in their classroom. Forty percent (n = 10) of teachers feel that they are not reaching
every student in their classroom with their mathematic instruction. The majority of teachers
17
(60%, n = 15) believe that they are reaching each student in their classroom during mathematic
instruction.
Agree 60%
Disagree 40%
Figure 2: Mathematics Instruction Meets Needs of Each Learner in Classroom (n=25)
Question number three asked teachers about the importance of differentiation as a method
for teaching. Eighty-four percent (n = 21) of teachers believe that differentiated instruction is
necessary for student success in math.
Agree 84%
Disagree 16%
Figure 3: Differentiated Instruction is Necessary for Student Success in Math (n=25)
18
The fourth question on the teacher survey asked if teachers felt prepared to differentiate
in the classroom. Thirty-two percent of teachers (n = 8) have the knowledge, tools, and support
to effectively differentiate math instruction. A majority of teachers, 68% (n = 17) felt they lacked
the knowledge, tools, and support to differentiate math instruction
Agree 32%
Disagree 68%
Figure 4: Knowledge, Tools, and Support (n=25)
The last question on the teacher survey was an open ended question asking teachers to
share any additional frustrations they had with teaching mathematics. Out of the 25 surveys
returned, 22 teachers responded to this question (88% response rate). Teachers at both Site A and
B responded that one of their main concerns is time. They do not have enough time for planning
differentiated math activities when they have a detailed curriculum to cover during the course of
the school year. Several teachers at the high school level indicated they are unsatisfied with the
idea of “teaching to the middle” because this leads to a lack of challenge for the advanced
students, while it frustrates the lowest students who usually end up needing a re-teaching lesson
anyway. Teachers at both sites were also unsure of what activities to give to accelerated students
who finish early; it is difficult to define the difference between challenging activities versus busy
work. A concern mentioned at the high school level was how to grade fairly; should grades be
19
based upon effort or performance? Several high school teachers expressed concern about
whether or not their students truly have a low ability when it comes to math, or are they just
being lazy and not putting in the proper amount of effort? Teachers at Site A commented that in
the primary grades many students are unable to complete numerous tasks independently. When
teachers are working with various small groups students need the skills to be able to work alone
without constant teacher guidance.
Student Survey
The purpose of this instrument was for the teacher researchers to gain understanding of
student interests and plan instruction based on these learning preferences. Students in each
teacher researcher’s classroom, who had parental consent to participate in this study, completed a
student survey. Because there are a wide variety of ages taking part in this study, this survey was
adjusted to be age appropriate for the students participating resulting in three different surveys
being used in the research project. Below will describe the results of the three surveys beginning
with Teacher Researcher A’s high school survey, then Teacher Researcher B’s kindergarten
survey, and then conclude with the results of Teacher Researcher C and D’s second grade
survey.
High School Survey
Out of 48 high school students in Teacher Researcher A’s two academic geometry
classrooms, 26 (54%) students consented to the project and were surveyed. Surveys were
completed in class once during pre-documentation on Monday, January 29, 2007. Students were
asked to rate six Likert scale questions, choosing from one (strongly agree) to four (strongly
disagree) and then were asked an open ended question asking about the students’ interest outside
of school. Please refer to Appendix B to view this survey.
20
Question one asked students if students learned better by working with other students. A
noteworthy 85% (n = 22) of respondents agreed with the statement compared to 15% (n = 4) of
respondents who disagreed. Please refer to Figure 5.
Agree85%
Disagree15%
Figure 5: Learn Better Working With Another Student or Groups (n=26)
Question two addressed whether students would rather write about math problems instead
of solving them problem by problem on a homework assignment was addressed by question two.
As demonstrated by Figure 6, students markedly disagreed (96%, n = 25). Only one student
would rather write about mathematical themes or problems than solve them.
Agree4%
Disagree96%
Figure 6: Would Rather Write About Math (n=26)
21
Question number three in the high school survey asked if students wished they could
work with the teacher in a small group if they were struggling with concepts. Sixty-nine percent
(n = 18) of the respondents agreed with the statement as illustrated in Figure 7.
Agree69%
Disagree31%
Figure 7: Wished to Have the Opportunity to Work with the Teacher (n=26)
The fourth question asked students if the material covered in the class was too easy.
Twenty-three percent (n=6) of students agreed with that statement compared to the majority
(77%, n = 20) who disagreed. Refer to Figure 8 below.
Agree23%
Disagree77%
Figure 8: Material Covered is Too Easy (n=26)
22
Next students were asked if talking about math was preferred to solving math problems.
A noteworthy majority disagreed with that statement at 81% (n = 21) and preferred to solve math
problems as they normally do as shown in Figure 9.
Agree19%
Disagree81%
Figure 9: Would Rather Talk About Math (n=26)
The last Likert scaled question inquired if the high school survey respondents were
curious how math is used in the world around them. Figure 10 demonstrates that the classes were
somewhat split. Fifty-four percent (n=14) disagreed about being curious about math’s application
in real life while 46% (n=12) agreed that they were curious.
Agree46%Disagree
54%
Figure 10: Curious about How Math is Used in Real Life (n=26)
23
Finally, the survey asked the students to briefly describe what kinds of activities the
respondents participated in outside of school on an average day, and in particular, what internet
sites they may visit or video games played. Figure 11 shows that the students’ most frequent
activity (n=12) was getting on the internet and communicating with other friends by email,
instant messaging, or communicating through popular websites such as Myspace. The second
most popular activity (n=8) for students after school is exercising by going to the YMCA,
participating in a school sport such as track and field, or working out by lifting weights. Another
popular pastime (n=7) for the high school students surveyed is playing all sorts of videogames
from football to war simulation games.
12
87
54
32 2
0
2
4
6
8
10
12
14
Intern
et
Exerci
se/Spo
rts
Video g
ames
Hang ou
t with
frien
dsWork
Talk on
phone
Shopp
ingRead
Activities
Num
ber o
f Stu
dent
s
Figure 11: What do you do after school? (n=43)
Kindergarten Survey
Out of 21 kindergarten students, 17 students completed the survey (81%). Surveys were
completed in class once during pre-documentation on Monday, January 29, 2007. Students in
Teacher Researcher B’s classrooms were asked to rate six questions, choosing a happy or sad
24
face (yes or no) to answer each one. Due to the age of the students, Teacher Researcher B
dictated the questions to the class. Please refer to Appendix C to view this survey.
The first question on the kindergarten survey asked students if they enjoyed playing math
games in class. One hundred percent (n = 17) of the students who filled out a survey indicated
they like to play math games, as shown in Figure 12 below.
Agree 100%
Disagree0%
Figure12: Like to Play Math Games (n=17)
The second question on the kindergarten survey inquired whether the students prefer to
work by themselves. The majority of kindergarten students (71%, n = 12) expressed that they
enjoy working independently. Figure 13 below displays the results of this question.
Agree 71%
Disagree29%
Figure 13: Like to Work By Myself (n=17)
25
The next question asked the kindergarten students if they enjoy using manipulatives such
as cubes, squares, and counters to solve math problems. Figure 14 below shows the majority
(82%, n = 14) of students stated they do like to work with manipulatives in math class.
Agree 82%
Disagree18%
Figure 14: Like Using Cubes, Squares, and Counters (n=17)
The fourth question on the kindergarten survey asked the students if they like to complete
math worksheets in class. A majority (59%, n = 10) of students indicated they do enjoy working
on worksheets. A close minority (41%, n = 7) of students do not enjoy completing worksheets, as
indicated in Figure 15 below.
Agree59%
Disagree41%
Figure 15: Like Math Worksheets (n=17)
26
The second to last question on the survey asked the kindergarten students if they feel that
math is easy for them. As indicated in Figure 16 below, the majority (71%, n = 12) of students
responded that they do feel math class is easy. Twenty-nine percent (n = 5) of the students feel
that math is not an easy subject.
Agree71%
Disagree29%
Figure 16: Math is Easy (n=17)
The final question on the survey asked the kindergarten students if they enjoy listening to
music while working in class. One hundred percent (n = 17) of the students in Teacher
Researcher B’s classroom indicated they like listening to music while completing assignments.
Please see Figure 17 below.
Agree 100%
Disagree0%
Figure 17: Like Listening to Music (n=17)
27
Second Grade Survey
Out of 48 second grade students, 36 students completed the survey (75%). Surveys were
completed independently once during pre-documentation on Monday, January 29, 2007.
Students in Teacher Researcher C and Ds’ classrooms were asked to rate seven questions,
choosing yes or no to answer each one. Please refer to Appendix D to view this survey.
The first question on the second grade survey asked if the students liked to work by
themselves. Reflected in Figure 18, the majority of second grade students (69%, n = 36)
expressed that they like to work alone.
Agree69%
Disagree31%
Figure 18: Work by Myself (n = 36)
The second question on the survey asked the students if they liked to work with a partner
or a group of kids. Showing a close relationship, the majority of students (54%, n = 20) like to
work alone, which correlates with the first question on this survey. Whereas, 44% (n = 16) of
students like to work with a partner. Please see Figure 19 below.
28
Agree44%
Disagree56%
Figure 19: Like to Work with a Partner (n = 36)
The third question in the survey asked the students if they liked to use counters, cubes,
and other math pieces. Students showed a preference to hands on learning. While completing
math problems, the majority of students (69%, n = 25) like to use math manipulatives, such as
counters and cubes. The minority (31%, n = 11) prefer to use other methods to problem solve.
Please see Figure 20 below.
Agree69%
Disagree31%
Figure 20: Like Using Counters, Cubes, and Math Pieces (n = 48)
29
On the fourth question, students were asked if they liked drawing pictures to help solve
math problems. As shown in Figure 21, they students were evenly divided. Half the students
preferred using pictures to solve math problems (50%, n = 18) and 50% (n = 18) of students do
not like to draw pictures to solve math problems.
Agree50%
Disagree50%
Figure 21: Like Drawing Pictures to Help Problem Solve (n = 36)
Question number five on the survey asked the students if they like to work on math
worksheets. As indicated in Figure 22, the majority of students (69%, n = 25) like to do math
worksheets. The minority (31%, n = 11) of students do not like to do math worksheets.
Agree69%
Disagree31%
Figure 22: Like Math Worksheets (n = 36)
30
On the sixth question, students were asked if they like to listen to music while they work.
Figure 23 shows that the majority of students (72%, n = 26) liked to listen to music while doing
their work. The minority (28%, n = 10) do not like to listen to music while they work.
Agree72%
Disagree28%
Figure 23: Like Listening to Music (n = 36)
The final question asked the students if they liked moving around while doing math. In
Figure 24, the graph shows that the majority (58%, n = 21) of students like to move around,
rather than the 42% of students (n = 15) who do not like to move around.
Agree58%
Disagree42%
Figure 24: Like to Move Around During Math (n = 36)
31
Observation Checklist
The teacher researchers completed a daily observation checklist during 10 consecutive
school days, beginning on Monday, January 29, 2007. The purpose of this tool is to record
students’ ability level by indicating if they were on task, finished with their work, or still needing
support five minutes after an assignment was given. Teacher researchers walked around the room
monitoring and recording the progress of each student. Once work was complete, teacher
researchers graded the student products. Student products were recorded as satisfactory or
unsatisfactory in the performance section of the observation checklist. Teacher researchers then
compared the observation checklist to student performance on the given assignments looking for
a correlation between student performance and application. A total of 773 observations took
place during the two weeks. Please refer to Appendix H to view a copy of the observation
checklist.
A majority (n = 427, 55%) of students were observed to be on task when an assignment
was given. Twenty-six percent (n = 198) of students indicated that they needed help by asking
questions or raising hands during the observation. When the assignments were graded, a
majority (n = 631, 82%) of students were completing work in a satisfactory manner.
32
427
148198
631
142
-
100
200
300
400
500
600
700
On Task Finished NeedingAssistance
Pass Fail
Behaviors
Num
ber
of S
tude
nts
Figure 25: Student Observations (n=773)
Pre- and Post-Tests
Teacher researchers administered this instrument before the beginning of each new unit
to assess prior knowledge of a topic. The identical test was then given again at the conclusion of
a unit as a post-test. The purpose of this tool was two fold. First, this tool documents the varied
ability of their students, in a very precise manner compared to the other tools, by focusing on
particular topics in each unit. Recognizing the strengths and weaknesses of their students helped
the teacher researchers guide instruction during the unit and differentiate instruction. Second and
more importantly, since the pre- and post-tests were identical, the teacher researchers compared
the results of each set of tests to see if student understanding increased due to differentiated
instruction. Since the largest benefit of this tool was to try and document the effectiveness of the
intervention, the teacher researchers decided to discuss all of the pre- and post-test data in the
Presentation and Analysis of Results section of the action research paper (see page 76).
33
Summary
Based upon the tools described above, the data shows the teacher researchers that
differentiation strategies may help to meet the multiple levels in today’s classrooms. The
surveyed teachers are feeling frustrated with varied abilities and they agree differentiation is
necessary (Figure 3), but they often do not have the tools or time to accomplish this task (Figure
4). All teacher researchers completed an observation checklist and concluded that there are
different levels of achievement in their classrooms (Figure 25). Along with the different levels of
achievement, time to complete a task varies among students (Figure 25). The student surveys
revealed that high school students like to work in groups (Figure 5) or if they are struggling they
would prefer to work with the teacher in a small group setting (Figure 7). The primary students
indicated they would like to work independently (Figure 13 and Figure 18). Students surveyed in
the primary grade levels enjoy listening to music while completing math problems (Figure 17
and Figure 23). Primary students also indicated a preference for completing worksheets as a form
of practice (Figure 15 and Figure 22). High school students indicated they prefer to spend time
after school on the Internet (Figure 11).
Reflection
Figure 6 demonstrates that high school students markedly preferred to solve problems
rather than write about problems. This data can lead to a problem, particularly in high school,
because students are required to copy many assignments out of the book for homework. In
addition, our data shows (Figure 9, Figure15, and Figure 22), and we concur, that worksheets are
a preferable activity for students in math class. These two sets of data lead us to alter our
differentiation strategies. First, we had originally planned to use all of the multiple intelligences
34
when implementing activities including writing. We may now disregard some of the writing
assignments as options for the students.
We were all surprised that the primary students prefer to work on their own (Figure 13
and Figure 19), and the high school students enjoy working with those around them (Figure 5).
We conclude that this is a representation of the social skills each age group. The younger
students do not have the skills to work cooperatively in a group. On the other hand, the older
students may prefer to work in groups to socialize rather than complete tasks. The surveys
reinforced our belief that most students enjoy manipulatives and games (Figure 12, Figure 14,
and Figure 20) as well as the internet (Figure 11). The student surveys are beneficial to the
teacher researchers in regards to planning activities around student interests. Based on the survey
results, all teacher researchers are planning to implement lessons using cooperative learning,
allowing for student choice, and hands-on activities.
The observation checklists reinforced the idea that teacher researchers need to find
alternative ways to reach all learners (Figure 25). Students are finishing work at different times
and those that are advanced need to be given enrichment activities that are worthwhile, so time
can be spent with struggling students. Teacher researchers believe that the numbers from the
observation checklists validate the problem of varied ability in the classroom. Twenty-six
percent (n = 198) of students need help while 19% (n = 148) were finished at the time the
observations were recorded.
I, Teacher Researcher B, have a difficult time believing the validity of the kindergarten
survey. I think my students preferred to color in the happy faces to just to satisfy me. Throughout
the 10 weeks of intervention, I plan to ask my students for feedback regarding their likes and
35
dislikes for various activities and lessons. This will allow me to validate their opinions
demonstrated on the survey.
All of the data collected demonstrates varied ability is prevalent in today’s classrooms.
We believe implementing differentiation strategies will help all students achieve their fullest
potential.
Probable Causes
While examining the problems of varied ability in the classroom, we must first examine
the issue through a wider lens and then we will work our way down to the actual classroom
itself. Schools in general are in either of two camps: mix the ability of the students together into
heterogeneous classrooms or separate students into different groups or tracks. The issue is far too
complex to assume that all schools choose one method or the other. In fact, research on the topic
provides no clear winner. A difficult choice must be eventually made by every school district as
to how much ability will be mixed together to achieve an acceptable balance of learning.
Homogeneous instruction is the most efficient way to teach content (Brimijoin, 2005) and
historically schools in the United States have been run on a factory model where all students
learn the same way and should achieve the same goals (Baglieri & Knopf, 2004). In the past,
teachers have seen their primary role in the classroom as the distributor of information. These
views are outdated because in most of today’s classrooms there is a wide range of abilities,
which makes it necessary for teachers to reevaluate their role in the classroom (Scholz, 2004).
It is unspoken that, in general, schools favor certain behaviors, thinking, knowing, and
interacting. Students who do not fit this protocol are identified for educational testing which
confirms abnormality and segregates them (Baglieri & Knopf, 2004). Schools are continually
identifying students with disabilities and qualifying them for special services. The schools need
36
to take responsibility to adjust the curriculum to the needs and levels of the students they serve
so that fewer students are being pulled from the regular education classroom (Tomlinson, 2005).
Especially if we think the larger purpose of any school is educate for a healthy democracy.
Schools should not isolate groups of students since they will all eventually be members of a
larger community when they graduate. Students should see other students’ viewpoints and
talents, good or bad, before going out into a democracy (George, 2005).
At the school wide level, there are many problems with both mixing all students together
and separating students into tracks based upon ability. On the one hand, some argue that
grouping all students into mixed ability classrooms does not challenge students enough
(Cramond, Benson, and Martin, 2002). On the other hand, some will argue that tracking students
does not necessarily guarantee all students’ success either (Burris & Welner, 2005; DiMartino &
Miles, 2005; Hallam, 2002; Lawrence-Brown, 2004). Either way, many studies have been
conducted on ability grouping and the results have been inconsistent (Hallam, 2002); neither
tracking nor heterogeneous grouping have shown to improve students’ test scores (Reed, 2004).
Whether or not a teacher today agrees with tracking students to cope with mixed ability
in the classroom, it is a reality in most classrooms and we should spend some time examining the
problems with tracking. Beginning in kindergarten most schools separate special needs from the
general population. By the time students reach high school, there may be five different ability
levels for mathematics that students are already tracked into. Research suggests that tracking
demonstrates no academic gain and even causes a wider gap between high and low students
(Johnson, 1999). Students in higher ability groups are usually successful, but lower ability
groups suffer (Hallam, 2002). Often the curriculum is watered down (Burris & Welner, 2005)
37
and teachers can begin to view the lower ability students as not being teachable or able to reach
their full potential (Atkins & Elsesser, 2003).
In schools where tracking is taking place, many teachers do not know how to
appropriately implement lessons that will reach all students and provide opportunities for each of
them to reach their full potential. They are also not receiving the proper guidance to help them
make these decisions. The reason one-size-fits-all classrooms continue is that teachers lack the
exposure and the knowledge to incorporate differentiated instruction (Edgemon, Jablonski &
Lloyd, 2006; Holloway, 2000; Tomlinson, 2005). Practicing teachers need training on how to
address the varying learning styles, interests, and abilities of the students in their classrooms so
they can implement differentiated instruction (Pettig, 2000; Wehrmann, 2000; Tieso, 2004).
Besides the veteran teachers, many new teachers are entering their first year of teaching without
the proper knowledge or tools of how to reach all learners. They are not adequately prepared by
their university for the variety of abilities and skill levels that are found in today’s classrooms
(Holloway, 2000). Educators need to update their teaching methods to provide differentiated
curriculum, instruction, and assessment (George, 2005). Many teachers find themselves teaching
a class in a content area in which they are not well versed. In addition, they are having trouble
finding appropriate resources, high level, and age appropriate material (VanTassel-Baska &
Stambaugh, 2005). Teachers are expected to cover the curriculum and prepare students to pass
standardized tests, but are often given little support (Tieso, 2004).
Now that we have touched on the problems that schools face with the varied ability of
their students, let us examine the affects on the classroom itself. If teachers can agree on one
thing it would be that, tracked or not tracked, there is still a large variety of ability in each
classroom. This diversity will only continue to grow (Maheady, 1991). The students have
38
different learning abilities, and different learning styles (Bowerman, 2005; Johnson, 1999).
Students arrive in the classroom with different levels of development, interests, and exposure to a
multitude of environments and experiences (Ferguson, 1999; VanTassel-Baska & Stambaugh,
2005). In addition, each student enters the classroom with a different expectation for the year
based upon past experiences. Some students need more time to work on things while others
might need more instruction and re-explanation (Johnson, 1999). Teachers struggle to find a
method of teaching to meet the diverse classroom needs because what works for some students
will not work for others (Brimijoin, 2005; DiMartino & Miles, 2005; Johnson, 1999; Reed,
2004).
Regardless of the differences in student ability, teachers must hold themselves as well as
their students responsible for learning in the classroom. Especially with the No Child Left
Behind Law which is placing a great deal of pressure on teachers and school administrators to
ensure that all students are successful learners (VanSciver, 2005). Consequently, educators are
increasingly faced with the challenge of creating an environment where all the needs of the
students can be met with a higher degree of accountability (Ferguson, 1999; Greenspan, 2005;
2000). Block teams have been implemented into some schools. This allows grade level teachers
to work together and share resources, curriculum planning, and teaching tasks (Ferguson, 1999).
57
Specialty teachers have also been included into these groups to help create curriculum that
includes strategies to help every student become successful. The regular education and special
education teachers are able to be resources for each other and to merge their talents (Carney et
al., 2003; Ferguson, 1999; Sacacore, 1997). Another option is to consider sharing the load of
differentiation by grouping students and trading groups for content area with another teacher.
This strategy is effective, it involves pre-assessing students, grouping them based on need, and
providing effective curriculum adjustments (VanTassel-Baska & Stambaugh, 2005). This
strategy allows groups of teachers to be collectively responsible for a class. Instead of having one
teacher per group of kids there are several. The teachers can pull together to help meet every
students’ needs (Ferguson, 1999). Volunteers and paraprofessionals can give teachers additional
support in the classroom (Ferguson, 1999; Sacacore, 1997). Administrators can provide
instructional support and suggestions for the teacher and paraprofessional on how to best utilize
and work with one another and the children (Dover, 2005).
Project Objective and Processing Statements
As a result of cooperative learning lessons, multiple intelligence based lessons, student
choice of assignments, and differentiated assignments during the period of January 29, 2007
through May 11, 2007, the students of Teacher Researchers A, B, C, and D, were to improve
mathematic skills in a varied ability classroom.
To implement the intervention for this research project, the teacher researchers focused
on four areas of differentiation. First, teacher researchers developed cooperative learning lessons
at each grade level. For example, teachers paired up high and low level students and introduced a
math game to review money concepts. Secondly, multiple intelligence lessons were implemented
in each classroom. For instance, second grade students used manipulative “cake slices” to
58
demonstrate fraction values while kindergarten students practiced counting by fives using a
clapping song with a partner. Teacher researchers also developed lessons utilizing student
choice. At the high school level, the teacher developed three different projects for students to
choose from to demonstrate proportion and scale change. Finally, differentiated assignments
were produced to reach each student at their particular level of mathematical ability. At the high
school level the teacher created three versions of a worksheet each with varying difficulty.
Project Action Plan
The following timeline outlines the implementation of the research project. Of the 14
weeks allowed for this project, 10 weeks of intervention took place from February 13th, 2007
through April 27th, 2007. The remaining four weeks, January 29th, 2007 through February 9th,
2007 and April 30th, 2007 through May 11th, 2007, were used for pre- and post-documentation,
and compiling information.
Week of January 22nd, 2007 – January 26th, 2007 Principal needs to approve parent permission forms. Xerox parent permission forms, teacher surveys and observation checklists. Pre-documentation Weeks: January 29th, 2007 – February 9th, 2007 Send parent permission and student assent forms home. Parent permission and student assent forms due back by February 6th. Make calls to obtain parent permission forms February 9th. Survey students for personal interests. Prepare activities for upcoming units using multiple intelligences. Distribute teacher surveys. Teacher surveys due back by February 5th. Begin pre-documentation daily student observation checklist. Week of February 13th, 2007 – February 16th, 2007 Compile data from student observation checklist. Administer pre-test of first unit. Review teacher surveys and collect data.
59
Teachers will reflect daily to assess the effectiveness of chosen interventions and plan accordingly.
Each researcher will differentiate math instruction using modified assignments, incorporating multiple intelligences, and cooperative learning.
Week of February 19th, 2007 – April 27th, 2007 Teachers will reflect daily to assess the effectiveness of chosen interventions and plan
accordingly. Each researcher will differentiate math instruction using modified assignments, incorporating
multiple intelligences, and cooperative learning. Each researcher will administer pre- and post-unit test when appropriate. Post-documentation Weeks: April 30th, 2007 – May 11th, 2007 Teachers will complete post-documentation daily student observation checklists. Each researcher will compare data from pre- and post-documentation checklists and interpret
results. Each researcher will compare data from pre- and post-tests and interpret results.
Methods of Assessment
The teacher researchers at Sites A and B used several pre- and post-tests as a part of
post-documentation. The purpose of this tool was to compare the pre- and post-test to see if
student understanding had increased due to differentiated instruction. The pre- and post-tests
were given by the teacher researchers as needed from February 13, 2007 through April 27, 2007
according to their individual classes. The teacher researchers used the tool by giving each of the
104 students in the intervention a pre-test. See Appendix E through G for sample pre-tests. The
students were then given the same test after the teachers had taught and implemented
differentiated instruction in their class. The pre- and post-tests were then compared to see if
student achievement increased.
The teacher researchers at site A and B completed two observation checklists that
included each consenting student in their classroom. One checklist was completed during pre-
documentation and the other one was completed during post-documentation. The purpose of the
60
first observation checklist was to record students’ ability level by indicating if they were on task,
finished with their work, or still needed support. This indicated that different abilities were
relevant in our classrooms. The purpose of the second observation checklist was to see if
differentiated instruction helped to bridge the gap of varied abilities. The first observation
checklist was completed during the weeks of January 29, 2007 through February 9, 2007. The
second observation checklist was completed during the weeks of April 30, 2007 through May 11,
2007. Post-data was compared to pre-data to document any change. Please refer to Appendix H
for the student observation checklist.
61
CHAPTER 4
PROJECT RESULTS
Reaching every student in an inclusion classroom was the problem identified by the four
teacher researchers. The teacher researchers encountered academic achievement that ranged from
high, medium, and low. The students that performed at a high academic level were often finished
with their work early and left unchallenged. The students that performed below average
academically needed constant support and redirection which took away from the teacher’s
instruction time. It appeared that the only students that were benefiting were the average
students.
Over the course of 10 weeks, the teacher researchers implemented four main
interventions into their classroom. The interventions consisted of cooperative learning lessons,
student choice of assignments, multiple intelligence based lessons, and differentiated
assignments. The participants in this study consisted of 79 students: 26 grade 10-12 high school
students, 53 kindergarten through second grade students, and 25 teachers for a total of 104
participants. This research project ran from January 22, 2007 through May 11, 2007.
Historical Description of the Intervention
At any given time throughout the school year, teachers are faced with students that have a
wide range of abilities. Instructing students using a one-size-fits-all approach is no longer
appropriate for today’s classrooms (VanSciver, 2005). In an effort to reach all learners,
differentiation strategies have become popular in recent years. The basic idea behind
differentiation is designing lesson plans, projects, assessments, and learning environments to
accommodate the individual readiness, interests, and learning profile of each student (George,
Each teacher researcher developed lessons and activities using multiple intelligences.
Teacher Researcher A used the visual-spatial intelligence when students explored parallel and
skew lines by drawing in perspective. This was an engaging lesson because it brought up topics
from art class and became cross-curricular. The students who were very interested in art were
given the opportunity to shine and share their knowledge with the class by defining such words
as horizon line and vanishing point. Teacher Researcher B used many of the multiple
intelligences during the entire research process. One example was when students were asked to
solve simple addition problems. Popped popcorn was set on the tables for the students to
demonstrate each addend. This was a very effective way to teach addition to kindergarten
students because the popcorn enticed each student into trying addition. When the students were
done with their addition worksheet, they were able to eat their popcorn. This particular activity
asked the students to use their hands to move the popcorn (bodily-kinesthetic) into place and also
allowed student to see (visual-spatial) the math problem in front of them. Teacher Researcher C
used bodily-kinesthetic through the use of manipulatives to teach various math concepts. During
one lesson students were asked to demonstrate their knowledge of place value by using
connecting cubes. This was a positive learning experience because the teacher could identify
which students understood the concepts and who needed additional help. Teacher Researcher D
used multiple intelligences when teaching students how to regroup. The activity began by
Teacher Researcher D writing a double digit addition problem on the board. Students were used
as the addends and Teacher Researcher D demonstrated how to regroup by moving the smaller
66
group to the larger group to make the next ten. This was a successful lesson for the students
because it allowed them to visualize the regrouping taking place.
The teacher researchers felt that the lessons using Gardner’s Multiple Intelligences were
very easy to implement in the classroom. Students were motivated by the various activities and it
was discovered that many students excelled in more than one multiple intelligence.
The idea of one teaching strategy or lesson fitting all students is not appropriate for
today’s classrooms. To actively engage and push each student to reach their fullest potential,
some accommodations must be made. One way to accommodate for the many levels in today’s
classrooms is to differentiate assignments to suit individual needs. This can be done as easily as
making a three-tiered practice worksheet. The lowest students would be responsible for
demonstrating a basic understanding of the concept while the higher achieving students would be
asked to synthesize the ideas. By making simple modifications to the application, the content is
still being taught and the student is being challenged at their individual level.
The final intervention of this research project was implementing differentiated
assignments. This intervention was aimed at reaching each student at his/her ability level with
the hope of increasing student performance. Teacher Researcher A differentiated a chapter
review assignment. A worksheet for lower level students was designed with a word bank with
only the words necessary to complete the assignment. Another worksheet had a word bank with
extra words; this was developed for the average ability students. The highest achieving students
received a worksheet that did not have a word bank. This proved to be a positive learning
experience for the students. When it came time to review the assignment with the class, Teacher
Researcher A was pleased that some of the low level students were able to answer the questions
that the higher students could not because they had the help of the word bank. This seemed to
67
increase student participation and confidence. When completing a chapter on money
identification and value, Teacher Researcher B designed a shopping activity for her kindergarten
students. Each student was able to select a classroom item he/she wanted to purchase and the
students were given pretend coins to buy their selected item. The higher level students were
given a combination of pennies, nickels, and dimes to shop with. The lower level students were
only given pennies to shop with so that they would not be overwhelmed. This activity was
successful because it allowed the students to move around the room and each student was within
his/her comfort zone when making a purchase. Teacher Researcher C used a challenge sheet for
students who were excelling at the math concepts. Students were asked to complete enrichment
activities based on the concepts covered. Students enjoyed the activities but became frustrated
because they did not have sufficient time to complete the activities. Teacher Researcher D
differentiated an assignment on regrouping. The low to medium students were given regrouping
problems as a practice activity. The above average students were given addition problems that
had one addend and the sum. The challenge was to calculate the missing addend. This was a
positive experience for all students because it demonstrated their individual strengths and
everyone was successful.
I, Teacher Researcher A, used the normal review day before a test to develop a worksheet
that implemented differentiated instruction. Normally I would use the same worksheet for the
entire class but I made three different versions of the same worksheet, each focusing on low,
middle, and higher achieving students. I then distributed them to the respective levels of students
in my class based on quiz scores from the chapter. Please see Appendix I for the three versions
of the worksheet. I differentiated the worksheet by adding or removing two things: a word bank,
and a similarity statement. The lower version included a word bank with the vocabulary words
68
that students would need to fill in the blanks of definition statements. The middle version also
included a word bank with words used to complete the statements, but it also had extra words as
distracters that made it more challenging. The higher level version had no word bank at all. I
think the lower ability students that would normally just skip the “fill in the blank questions”
took the time to look through the word bank and truly try and answer the questions rather than
just give up and leave them blank. Also, when it came time to go over the answers to the
vocabulary statements, the lower achieving students got the opportunity to say the answer and
feel proud of themselves because the highest achieving students were completely stumped and
could not blurt out the answer first. The second way I made the worksheet more challenging was
that I left off the similarity statements for the similar figures for the practice problems on the
second page. The higher achieving students had to write their own statement or deal without it
while the lower achieving students could refer to the statement to help them set up proportions
and solve for missing sides. By including the similarity statements, it effectively removed one
step to the problem but still asked students to demonstrate they knew how to use proportions to
solve for sides of similar objects. This helps avoid discouraging students that are more likely to
make a small mistake with the set up and get an entire problem wrong even if they understand
and can correctly do most of the problem.
One specific lesson I, Teacher Researcher B, implemented in my kindergarten classroom
focused on simple addition. I designed this particular activity to incorporate student interests by
using multiple intelligences. I also differentiated the problems my students were given to
accommodate the variety of ability levels. Prior to introducing this lesson, I wrote a math
problem on a sentence strip for each student in my class. The problems varied in difficulty from
0 + 0 up to 10 + 10. Each problem was labeled with a student name which easily allowed me to
69
distribute the assignment. After I briefly reviewed the concept and vocabulary of addition, the
students were asked to color and cut out a picture of a ladybug. Then, they were given a piece of
construction paper that already had their addition problem attached to it. After gluing down the
ladybug, each student was given black paint and asked to paint the correct number of spots on
each wing of the ladybug using the addends in their problem. When they were done painting,
they were asked to count the number of spots and write the answer to their addition problem on
sentence strip. We covered each answer with a leaf and proudly displayed the ladybugs in the
hallway for other students to practice their addition.
I believe each student enjoyed this lesson. The students who usually struggle with
addition were able to easily complete this assignment with little assistance. The students who
were given the problems with higher numbers enjoyed the challenge. Each student successfully
solved their math problem by counting up the number of spots on their ladybug. I feel this lesson
was beneficial because it allowed my students to move around and be creative while they
worked. Also, by designing the problems to meet the students at their at their particular ability
level, it allowed each student to comfortably and confidently finish the assignment. Please refer
to Appendix J to view a student example of this assignment.
I, Teacher Researcher C, incorporated multiple intelligences, student choice, and adapted
the lesson using the Challenge Sheet found in Appendix K. The Challenge Sheet was given to
students who excelled at the material being covered. These sheets were given out on a weekly
basis. Students were first asked to complete a certain number of questions from the material
covered. Once the required work was finished, students were given six choices of enrichment
activities. These six choices related to different intelligences and gave the students an
opportunity to apply the math concept.
70
While we were working on place value, one student chose the card game option. This
student made up a game similar to ‘War’ with a twist. Two cards were flipped over and students
were to add the numbers together. Once the numbers were added, students had to identify how
many tens and how many ones were in their answer. For example, 5 + 7 = 12 this would be one
ten and two ones. As a challenge, they made the ace cards worth 100. I thought this was a great
game and implementation of using the math concepts.
I liked using the Challenge Sheet because I could give my attention to the struggling
students while the excelling students had something meaningful to keep them occupied. The
Challenge Sheet did not require additional planning or preparation on my part and was easy to
implement. I also think there were drawbacks to using the Challenge Sheet. My first concern was
that students did not have enough time to finish the challenge activities during the allotted time.
Finding time for students to work on finishing the activities proved to be difficult. I would have
liked to give every student an opportunity to try the Challenge Sheet. Unfortunately, with the
varied abilities, struggling students were unable to complete the activities because they needed
additional help with the basic concepts.
The Challenge Sheet did leave me with a few questions to ponder. The Challenge Sheet
would give struggling students an opportunity to use the math concepts in a new way, which I
believe would help them to understand the ideas better. This could be used as a collaborative
learning activity, pairing high and low students, to help one another. I think that I would like to
try using the Challenge Sheet again next year, but I will not use it for only excelling students. I
would like to use the Challenge Sheet as a morning activity that students can work on each day.
This will give each student the opportunity to be creative with the math concepts and build
understanding.
71
I, Teacher Researcher D, used ability folders, found in Appendix L as one way to
implement differentiated instruction in my math class. At the beginning of the week each student
was given a folder that included re-teaching or enrichment activities. There was an activity for
each lesson that was going to be taught that week. The re-teaching activities were given to
students that needed more support and the enrichment activities were given to the students that
were on level or needed a challenge. The students would keep these folders in their desk and
complete them when the lesson had been taught. Each week new activities would be placed in
the student’s folders. This activity seemed to work well for the students. It gave them confidence
because they were able to complete the activities in the folder independently and successfully.
Along with the activity folders being successful for the students, it was also successful for me. It
allowed me to pull students that needed more one-on-one support. I look forward to using this in
the future.
I, Teacher Researcher A, found that implementing semi-regular lessons involving
differentiated instruction can be an effective best practice in some classrooms. During my first
five years teaching, I struggled to get a firm grasp of the curriculum and hone my classroom
management skills. I thought that an effective teacher had students in rows, in their seats, taking
notes off the board and that automatically equated to learning. It was only recently that I have
tried to improve my classroom instruction and alter my dependence on teacher-centered delivery
of curriculum. Lecturing bores many students and taking notes off the board does not necessarily
mean students are paying attention and, most importantly, learning. I assumed that “that is the
way I learned best so this is the best way to teach.” Rather, some students learn best from peers,
from hands-on activities, discovery activities, or even just doing the homework problems.
Differentiated instruction addresses this difference in student learning and adds variety to the
72
classroom to keep students interested. With that being said, I do not believe that it can be
effective in every situation and it is not the ultimate teaching technique. The reality of trying to
differentiate the entire curriculum is very difficult though and I agree with Wehrmann when she
advocates taking baby steps toward differentiation and slowly building up your resources (2000).
During the intervention, I differentiated just two classrooms of lower level students and the
difference between the two classes when I tried to do particular differentiated lessons was
enormous. One class could not handle the computer lab because of maturity issues while the
other class preferred to learn through lecture and wanted me to tell them the relationships with
given quadrilaterals. Sometimes it depended on the day of the week, not just the class. For
instance, on a Monday when the students are quiet and focused, I would rather do a lecture. On a
Friday when the students are rambunctious, I would love to do a multiple intelligence based
discovery activity. Implementing this intervention has given me more practice evaluating
different classrooms as well as individual student needs and strengths. Being flexible is
something that I have always counted as a strength of mine and I believe that this challenging
project made me get out of my comfort zone and challenged me to experience another method of
delivering content to my students.
Throughout the 14 weeks of this project I, Teacher Researcher B, feel I have learned a
great deal in regards to what my students enjoy about math. Prior to implementing this research
project in my classroom, I would feel guilty if an administrator walked into my room and I was
not formally teaching my students. I now know it does not take a worksheet to validate that I am
teaching a concept to my students. I discovered that even though a game is being played,
learning is taking place. My five and six year old students enjoy playing math games. It does not
matter what topic the game is about or who they are paired up with, they love it. They enjoyed
73
the games so much that I was asked several times throughout this research project if they could
play them again. I also found that my students were eager to participate in math knowing that
they were not going to be sitting and completing a worksheet each day. The activities I
introduced that allowed for movement and used manipulatives were typically the most
successful. Five and six year old students need the opportunity to move, and giving them the
choice of manipulatives allowed my students to comfortably complete activities on their own.
Throughout this research project, I was teaching what I consider to be difficult concepts for
kindergarten students to comprehend: telling time and money. By developing as many hands-on
activities as possible, I believe my current students performed better than my students in
previous years.
When I began to research the solutions to varied ability, I was excited to learn about the
many aspects of differentiation and the opportunity to implement ideas with my students. I
quickly discovered that it would not be as easy as I initially thought. Finding appropriate
planning time to differentiate my math lessons was difficult. Also, I wanted to allow my students
freedom to select which math activities interested them. I did this by developing several math
centers and allowed my students to decide what activity they preferred. Allowing for several
choices of activities led to a problem; my students constantly needed reminders to stay on task.
Many students also had trouble remembering the directions of the different activities and
unfortunately at this age they are not able to read directions independently. This led to many
interruptions during the time I had hoped to work with lower level students. After two weeks of
trying many activities with student choice, I began to focus my attention on differentiated
assignments, multiple intelligences, and cooperative learning activities. That decision positively
74
impacted the remaining eight weeks of the research project. I felt more relaxed and the students
were able to complete activities with less confusion.
As I spent time reflecting on my weeks of research, I do feel that differentiation can be a
very positive, and at times frustrating, way to instruct students at their individual levels.
However, when implementing differentiation strategies, it is important that teachers do not take
on more than they can actually handle. I have learned to begin small, with one unit of study, and
as you become more comfortable, expand the amount of differentiation strategies you use with
students. The knowledge and ideas I have gained throughout this research process will give me
the opportunity to be a better educator for my future students.
As a result of implementing this project and these interventions I, Teacher Researcher C,
feel that there are some aspects of my teaching that have been affected. For me this has been a
very challenging and sometimes frustrating process. Lack of planning time, resources, support,
and classroom management knowledge left me feeling inadequate to successfully differentiate at
various levels. These were some of the same problem areas that were found by other researchers.
My first struggle was planning time. I was only differentiating for one subject and found myself
needing more time to plan. Being a primary teacher, and teaching all subjects, I cannot imagine
the amount of time it would take to differentiate for each subject. There has to be an easier way
to plan and make differentiation successful and possible. Classroom management was another
struggle. Planning activities to successfully engage all students in meaningful activities was
extremely difficult. It was hard for me to be working with a small group while other students
would be done and asking what they should do next. Another aspect was timing; trying to find
activities that would be able to be completed by different students in an allotted amount of time.
Some of the challenge activities required more than one class period; while the regular classroom
75
work could be completed quickly. I felt success and failure with using differentiation in my
classroom. My students and I loved using cooperative learning. Working together is a lifelong
skill that I feel needs to be introduced and used in education. When students work together they
learn how to problem solve and compromise. They can help each other learn and sometimes
explain the concept in ways I did not think of. I plan on continuing using cooperative learning
strategies throughout my classroom. Hands-on learning was another area I felt was successful.
This brought some excitement and motivation into our classroom and gave us a break from the
norm of the traditional classroom environment. Students loved the hands-on approach. I felt that
using manipulatives helped students to grasp abstract ideas and make them more concrete. In my
opinion, the idea of differentiation in a classroom is just an idea for now. It sounds good on
paper, but the practicality of it is so challenging! I would love to meet a teacher who has
successfully differentiated and would be able to mentor and help me to make this a reality in my
classroom. I do believe that differentiation is necessary. With the wide range of abilities and
inclusive classrooms, whole-group instruction will not help all students to be successful.
I, Teacher Researcher D, have always been challenged with meeting the specific needs of
every student in the classroom. It was not until I implemented this project, that I truly saw some
light at the end of the tunnel. From the beginning, the literature gave me encouragement. I was
relieved to see other people out there that were struggling with the same problem. It was also
reassuring that there were many solutions that I could implement in my classroom. Suddenly,
differentiating instruction became a little bump in the road as opposed to a mountain.
There were several encouraging things that I observed while implementing differentiated
instruction in my math class. The first thing that stood out was that the students were excited
when it was time for math. I saw my unmotivated students become motivated. It seemed as
76
though they were almost assured that they would understand the lesson that was going to be
taught to them. Next, test scores improved, especially with the students that tend to struggle
academically. I think that they were really able to benefit from the small grouping with mixed
abilities. Finally, I was able to get a chance to challenge the high students. Without
differentiating instruction it is really hard to make sure that they stay motivated. In the future, I
look forward to differentiating other subject areas.
On the flip side, differentiating instruction does not come easy. It was very time
consuming and I often found myself overwhelmed. I found that my weekly planning took me
twice as long just to differentiate instruction in math; I could not imagine differentiating
instruction for all subject areas. In theory this is a good idea but it is certainly not realistic for one
teacher to do by themselves in a classroom with 27 kids. I will continue to use differentiated
instruction in my classroom in hopes that the practice and experience will make it less of a
challenge.
Presentation and Analysis of Results
The purpose of the research was to increase mathematical performance in a varied ability
math classroom. Our post-documentation data was looking to validate the fact that multiple
abilities existed in the classroom and the challenges this presented for inclusion teachers. The
problem of varied abilities appeared to be an issue among the four teacher researchers. During
the two weeks of pre-documentation between January 22, 2007 through February 9, 2007 the
teacher researchers at both sites copied and distributed the teacher surveys. Fifteen primary
teachers at Site A and 17 high school teachers at Site B were given the survey. Please refer to
Appendix A for a copy of the teacher survey. Each teacher had two weeks to anomalously
complete the survey. The results of the surveys were compiled at the end of the second week.
77
Parent permission forms were sent out during the two weeks of pre-documentation. Each
teacher researcher began a 10 day observation checklist. Please refer to Appendix H to view a
copy of the observation checklist. This checklist noted how many students were finished, on
task, or still needing assistance five minutes after a math assignment was given. The children
who did not receive permission to participate were eliminated from the observation checklist.
Each teacher researcher found the observation checklist to be time consuming. Teacher
researcher C felt that the students were showing the same ability levels daily and there was better
overall performance when students understood the concepts covered.
Each teacher researcher developed an age appropriate student survey. The purpose of the
survey was to find out the interests of the students. Please refer to Appendix B, Appendix C, and
Appendix D to view a copy of each survey. Twenty-six high school, 36 second grade, and 17
kindergarten students participated in the surveys. The teacher researchers enjoyed reading the
results of the student surveys. It was interesting to learn about the preferred activities of each
grade level. Teacher Researcher B felt that her students were selecting the happy faces on each
question just to please her. This raised questions regarding the validity of the kindergarten
survey.
It was noted by all teacher researchers that the students who did not turn in a consent
form were primarily the students who struggle academically and perhaps do not have parental
support.
Observation Checklist
The teacher researchers completed a daily post-observation checklist during 10
consecutive school days, beginning on Monday, April 30, 2007, which was identical to the
observation checklist done during pre-documentation. Teacher researchers recorded students’
78
behavior by indicating if they were on task, finished with their work, or still needing support five
minutes after an assignment was given. Once work was complete, teacher researchers graded the
student products they were recorded as satisfactory or unsatisfactory. A total of 718 observations
took place during the two weeks. Please refer to Appendix H to view a copy of the observation
checklist. A majority (64%, n = 463) of students were observed to be on task when an
assignment was given. Twenty percent (n = 142) of students indicated that they needed help by
asking questions or raising hands during the observation. When the assignments were graded, a
majority (88%, n = 629) of students were completing work in a satisfactory manner.
As demonstrated in Figure 26 below, when comparing the pre-observations to the post-
observations, the number of students that were on task increased after the intervention took
place. Conversely, the number of students needing assistance decreased as did the amount of
unsatisfactory work being turned in.
55%
19%26%
82%
18%
64%
16% 20%
88%
12%
0%10%20%30%40%50%60%70%80%90%
100%
On Task Finished NeedingAssistance
Pass Fail
Pre-ObservationPost-Observation
Figure 26: Observations Before and After Intervention (n=1491)
Pre- and Post-Tests
Teacher researchers administered this instrument before the beginning of each new unit
to assess prior knowledge of a topic. This instrument was given again at the conclusion of a unit
79
as a post-test. Pre- and post-tests were identical and compared to see if student understanding
increased due to differentiated instruction. Teacher researchers used this tool to guide instruction,
look for areas of weakness and strength. Pre-test questions differed for each researcher
depending on the curriculum to be covered. Please refer to Appendix E through G for Teacher
Researcher A through Ds’ pre/post-tests, respectively.
When compiling all pre- and post-test data as Figure 27 illustrates, there is a marked
increase from pre- to post-test scores. The average score increase for all teacher researchers from
the first test to the second is 35%.
50%
85%
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Combined Average Pre-Test Scores Combined Average Post-Test Scores
Figure 27: Pre- Versus Post-Test Scores (n=461)
Conclusions and Recommendations
After reviewing the results of our pre- and post-test data we noticed a noteworthy change
in student performance. Looking at scores across the grade levels, during pre-testing the average
score was 50% while post-test scores averaged 85%. However, we are unable to determine if
80
student success was based on interventions or the fact that the teachers had covered the concepts
with the class between testing. Since the pre-tests focused on concepts that had not been covered
it is believed that presenting the material will inevitably lead to student progress.
It was noted that students were very uncomfortable during pre-testing. This was
demonstrated in their behaviors of relying on students around them, complaining, and second
guessing their abilities. During pre-testing, some students thought they knew how to solve a
problem and made-up their own steps. This caused a conflict when teachers were presenting the
correct way to problem solve because some students reverted back to their own “made-up” steps.
Pre-testing also led higher students to thinking they did not have to participate during class
because they thought they passed the pre-test and understood the material. Due to a concern
regarding a possible lack of participation, pre-tests were never handed back to students.
Looking at the observation checklist there was a 9% increase in on task behavior (Figure
26) and a 3% decrease in off task behavior. This change is attributed to the fact that students
were engaged through cooperative learning during many activities. It is believed that when
students are engaged in learning they are more likely to participate and stay focused. There was a
6 % decrease in students needing assistance; we credit this change to students working in groups
and assisting one another. There was a 6% increase in satisfactory work; we believe this is due to
the fact that some students are more comfortable asking questions to peers rather than a teacher.
It is also believed that students can relate better to one another, often using more simplistic terms
to explain concepts. We believe cooperative learning positively impacted student progress and
we plan to continue implementing this strategy.
Overall, student performance increased. This leads us to believe that our interventions
were effective in some way. We cannot credit this solely to differentiation because there is no
81
way to evaluate or compare it to another teaching strategy, unless we were to undertake another
research project. As previously noted, students come into our class with different learning
experiences and prior knowledge. Students may have performed better on pre- and post-testing
because of a previous exposure to material rather than the differentiated interventions that were
implemented. The results of the interventions can also be related to the time of the year and the
curriculum covered. Curriculum concepts build on one another and later in the year students are
usually asked to recall previously learned material and apply it to new concepts. Students are
more familiar with the material which may lead to an increase in achievement. Also, our pre-
observations were started before spring break when students are less focused on academic. This
may have led to the increase in student performance we saw in our post-observations.
Having this experience has given us more knowledge and a starting point for
implementing differentiated instruction in our classrooms. We have decided to eliminate pre- and
post-testing in the future in an effort to eliminate unnecessary stress and/or confusion. Teachers
can use informal anecdotal records to monitor student progress rather than administering a pre-
test. A post-test should still be used to formally assess student progress.
In conclusion, we would like to continue to implement differentiation in our classrooms.
With the varied abilities in today’s classroom it is necessary to adapt teaching methods to meet
different needs. This is something that cannot be implemented immediately and needs to be well
thought out, planned, and gradually implemented. We felt the frustrations of planning time, time
allotted for activities in the classroom, and changing teaching styles in the middle of the year.
We feel these frustrations can be alleviated through proper training and resources.
82
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Please answer the following questions based upon how you feel when teaching mathematics to your students. Your completed survey can be turned into ________’s mailbox. Grade Level Taught: ____ 1. There is a wide range of mathematic ability in my classroom.
1 2 3 4 5
Strongly Agree Agree No Opinion Disagree Strongly Disagree
2. My mathematic instruction meets the needs of each learner in my classroom.
1 2 3 4 5
Strongly Agree Agree No Opinion Disagree Strongly Disagree 3. Differentiated instruction is necessary for student success in math.
1 2 3 4 5
Strongly Agree Agree No Opinion Disagree Strongly Disagree 4. I have the knowledge, tools, and support to effectively differentiate my math instruction.
1 2 3 4 5
Strongly Agree Agree No Opinion Disagree Strongly Disagree
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5. What frustrations do you have when teaching math to the various abilities in your class? Please use the back for any additional comments Thank you!
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Appendix B
Student Survey Name___________________ Period_____ I learn better by working with another student or groups of students Strongly Agree Agree Disagree Strongly Disagree 1 2 3 4 I would rather write about math than solve math problems Strongly Agree Agree Disagree Strongly Disagree 1 2 3 4 I wish I had the opportunity to work more with the teacher in a small group when I don’t get it Strongly Agree Agree Disagree Strongly Disagree 1 2 3 4 The material covered in this class is too easy and I can do everything by myself Strongly Agree Agree Disagree Strongly Disagree 1 2 3 4 I would rather talk about math than solve math problems Strongly Agree Agree Disagree Strongly Disagree 1 2 3 4 I’m curious how math is used in real life Strongly Agree Agree Disagree Strongly Disagree 1 2 3 4
Briefly describe what you usually do after school. Include the type of video games you might play, or internet sites you might visit, etc…
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Appendix C
Kindergarten Student Survey
Name______________________________ 1) I like to play math games. ☺
2) I like to work all by myself. ☺ 3) I like using cubes, squares, and counters during math class. ☺
4) I like to do math worksheets. ☺ 5) I think math is easy. ☺
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6) I like to listen to music when I work. ☺
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Appendix D
Second Grade Student Survey
Name: _________________ 1. I like to work by myself.
YES NO
2. I like to work with a partner or a group of kids.
YES NO
3. I like to use counters, cubes, and other Math pieces.
YES NO
4. I like to draw pictures to help me solve a Math problem.
YES NO
5. I like to do Math worksheets.
YES NO
6. I like to listen to music while I work.
YES NO
7. I like to do Math that involves me moving around.
YES NO
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Appendix E
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Appendix F
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Appendix G
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101
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Appendix H
Observation Checklist – Pre-Documentation
Day On Task Finished Needing Assistance
Performance
1
2
3
4
5
6
7
8
9
10
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Appendix I
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106
107
108
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Appendix J
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Appendix K
Name: __________________
* Challenge Sheet *
Must Do …
Do Number ____________________________ on page __________
Do Number ____________________________ on page __________
When finished, choose an activity …
o Make up a shopping trip to the mall. Use the concepts
presented in the lesson.
o Write a song that includes the math from this lesson.
o Write up questions about the math lesson, and ask someone in
the class to answer them. Write down his or her answers.
o Write a paragraph about how you felt about the math concepts
from this lesson. Where they easy? Hard? How did you figure
them out?
o Draw a book cover for a math book based on this lesson. Be
sure to include a title and illustrations that include the specific
topic of the lesson.
o Make up a card game that includes the concepts from the
lesson. The concepts might be used in the process of playing or